Frequency-dependent fluctuation-dissipation relations in granular gases
arXiv:0712.0779 · doi:10.1103/PhysRevE.77.051301
Abstract
The Green-Kubo relation for two models of granular gases is discussed. In the Maxwell model in any dimension, the effective temperature obtained from the Green-Kubo relation is shown to be frequency independent, and equal to the average kinetic energy, known as the granular temperature. In the second model analyzed, a mean-field granular gas, the collision rate of a particle is taken to be proportional to its velocity. The Green-Kubo relation in the high frequency limit is calculated for this model, and the effective temperature in this limit is shown to be equal to the granular temperature. This result, taken together with previous results, showing a difference between the effective temperature at zero frequency (the Einstein relation) and the granular temperature, shows that the Green-Kubo relation for granular gases is violated.
6 pages
References in corpus (26)
- Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
- Observing Brownian motion in vibration-fluidized granular matter
- Multiscaling in Infinite Dimensional Collision Processes
- Edwards measures for powders and glasses
- Shearing a Glassy Material: Numerical Tests of Nonequilibrium Mode-Coupling Approaches and Experimental Proposals
- The Einstein relation generalized to non-equilibrium
- Computer simulation of uniformly heated granular fluids
- Fluctuations and Rheology in Active Bacterial Suspensions
- Simulations of Pattern Formation in Vibrated Granular Media
- Edwards' measures: a thermodynamic construction for dense granular media and glasses
- Observable-dependence of fluctuation-dissipation relations and effective temperatures
- Fluctuation-Dissipation relations in Driven Granular Gases
- Experimental study of the Fluctuation-Dissipation-Relation during an aging process
- Effective Temperatures in Driven Systems: Static vs. Time-Dependent Relations
- Violation of the Einstein relation in Granular Fluids: the role of correlations
- Temperature probes in binary granular gases
- An exactly solvable model for driven dissipative systems
- Origin of the Violation of the Fluctuation-Dissipation Theorem in Systems with Activated Dynamics
- On the Einstein relation in a heated granular gas
- Transport coefficients for inelastic Maxwell mixtures
- What is the temperature of a granular medium?
- Fluctuation-dissipation relations in driven dissipative systems
- Fluctuation-Dissipation Ratio for Compacting Granular Media
- Simulations of dense granular gases without gravity with impact-velocity-dependent restitution coefficient
- Energy distribution and effective temperatures in a driven dissipative model
- Extended Einstein relations with a complex effective temperature in a one dimensional driven lattice gas
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- Equilibrium-like behavior in far-from-equilibrium chemical reaction networks
- A handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics
- Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
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